Sleptons, neutralinos and charginos were searched for in the context of sce
narios where the lightest supersymmetric particle is the gravitino. It was
assumed that the stau is the next-to-lightest supersymmetric particle. Data
collected with the DELPHI detector at a centre-of-mass energy near 189 GeV
were analysed combining the methods developed in previous searches at lowe
r energies. No evidence for the production of these supersymmetric particle
s was found. Hence, limits were derived at 95% confidence level.